Question:medium
Let the domain of \( f(x) = \log_3 \log_3 \log_7 (9x - x^2 - 13) \) be (m, n). Let the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) have eccentricity \( \frac{n}{3} \) and latus rectum \( \frac{8m}{3} \). Then \( b^2 - a^2 \) is equal to :
Let the domain of \( f(x) = \log_3 \log_3 \log_7 (9x - x^2 - 13) \) be (m, n). Let the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) have eccentricity \( \frac{n}{3} \) and latus rectum \( \frac{8m}{3} \). Then \( b^2 - a^2 \) is equal to :
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For \( \log_a(\log_b(x))>0 \), remember it simplifies to \( \log_b(x)>a^0 \), which is \( \log_b(x)>1 \), and finally \( x>b^1 \).
Updated On: Mar 3, 2026
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The Correct Option is D
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